Japan Advanced Institute of Science and Technology

JAIST Repositoryhttps://dspace.jaist.ac.jp/

TitleSingle-particle excitation of core states in

epitaxial silicene

Author(s)

Lee, Chi-Cheng; Yoshinobu, Jun; Mukai, Kozo;

Yoshimoto, Shinya; Ueda, Hiroaki; Friedlein,

Rainer; Fleurence, Antoine; Yamada-Takamura,

Yukiko; Ozaki, Taisuke

Citation Physical Review B, 95(11): 115437-1-115437-7

Issue Date 2017-03-28

Type Journal Article

Text version publisher

URL http://hdl.handle.net/10119/14718

Rights

Chi-Cheng Lee, Jun Yoshinobu, Kozo Mukai, Shinya

Yoshimoto, Hiroaki Ueda, Rainer Friedlein,

Antoine Fleurence, Yukiko Yamada-Takamura, and

Taisuke Ozaki, Physical Review B, 95(11), 2017,

115437-1-115437-7. Copyright 2017 by the American

Physical Society.

http://dx.doi.org/10.1103/PhysRevB.95.115437

Description

PHYSICAL REVIEW B 95, 115437 (2017)

Single-particle excitation of core states in epitaxial silicene

Chi-Cheng Lee,1 Jun Yoshinobu,1 Kozo Mukai,1 Shinya Yoshimoto,1 Hiroaki Ueda,1 Rainer Friedlein,2,* Antoine Fleurence,2

Yukiko Yamada-Takamura,2 and Taisuke Ozaki11Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan

2School of Materials Science, Japan Advanced Institute of Science and Technology (JAIST), 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan(Received 12 October 2016; revised manuscript received 28 February 2017; published 28 March 2017)

Recent studies of core-level x-ray photoelectron spectroscopy (XPS) spectra of silicene on ZrB2(0001) werefound to be inconsistent with the density of states (DOS) of a planar-like structure that has been proposed as theground state by density functional theory (DFT). To resolve the discrepancy, a reexamination of the XPS spectraand direct theoretical access of accurate single-particle excitation energies are desired. By analyzing the XPS datausing symmetric Voigt functions, different binding energies and their sequence of Si 2p orbitals can be assignedfrom previously reported ones where asymmetric pseudo-Voigt functions are adopted. Theoretically, we haveadopted an approach developed very recently, which follows the sophisticated � self-consistent field (�SCF)methods, to study the single-particle excitation of core states. In the calculations, each single-particle energyand the renormalized core-hole charge density are calculated straightforwardly via two SCF calculations. Bycomparing the results, the theoretical core-level absolute binding energies including the splitting due to spin-orbitcoupling are in good agreement with the observed high-resolution XPS spectra. The good agreement not onlyresolves the puzzling discrepancy between experiment and theory (DOS) but also advocates the success of DFTin describing many-body interactions of electrons at the surface.

DOI: 10.1103/PhysRevB.95.115437

I. INTRODUCTION

Two-dimensional materials are promising for the nextgeneration of technology and have been extensively studied[1–9]. Among them, research on silicene has caught greatattention since its successful fabrication on metallic substrates[3–9]. The recent formation of isolated quasi-freestandingsilicene showing the feature of massless Dirac fermions furthermarked considerable progress [10]. As expected, densityfunctional theory (DFT) [11,12] has provided substantialsupport for understanding silicene [3–10]. In the case ofsilicene on ZrB2(0001) [9], the DFT-proposed ground state,the planar-like silicene [13] as shown in Fig. 1(a), can wellreproduce the valence band structure measured by the angle-resolved photoelectron spectroscopy via the interpretation ofKohn-Sham eigenvalues as quasiparticle energies [14–16].However, the core-level x-ray photoelectron spectroscopy(XPS) [17–21] spectrum of silicene on ZrB2(0001) was foundto be consistent with the density of states (DOS) of Kohn-Shamorbitals of a buckled-like structure, not the planar-like one[9,22]. This is puzzling and implies that the underlying physicsin the core-level XPS spectrum is beyond what the DOScan offer, showing a need of theoretical access of accuratesingle-particle excitation energies.

The core-level excitation has been theoretically studied inthe past decades [23–35]. A sophisticated method to accessthe excitation energies is to perform the so-called � self-consistent field (�SCF) calculations, where each excitationenergy is obtained by the energy difference between the groundstate and an excited state via two self-consistent calculationsfrom first principles [23–34]. In the studies of single-particleexcitation of core states, another accurate but time-consuming

*Present address: Meyer Burger (Germany) AG, An der Baumschule6-8, 09337 Hohenstein-Ernstthal, Germany.

approach is to perform the quasiparticle calculation in theframework of diagrammatic perturbation theory within theGW approximation [15,35]. In principle, both approaches tothe core-level single-particle excitation energy should reachthe same result that corresponds to the total energy differencebetween N and N − 1 electrons of a system, as given by thepole of the electronic one-particle Green’s function [15,35].Owing to the complicated many-body interaction of electrons,such as the effect of core-hole screening, it is still challengingto calculate the single-particle excitation energies of core statesthat can directly be used to compare with the XPS experiments.

We follow the thrust of DFT that promises to give the totalenergy and charge density of an interacting many-electronsystem to study the core-level single-particle excitation insilicene on ZrB2(0001) for both the planar-like and buckled-like forms by directly calculating the total energies of systemswith/without a core hole using the method developed veryrecently [36]. The method resembles the sophisticated �SCFmethods. Specifically, the designated core hole is introducedby adding a penalty functional through a projector. Theinteraction between periodic images of the created corehole imposed by the periodic boundary condition is avoidedusing an exact Coulomb-cutoff technique [36,37] so that thecalculations can reflect the nature of the “N − 1”-electronsolid-state system. The calculated absolute binding energies ofcore states in the planar-like silicene are found to be consistentwith the reanalyzed experimental data. The core holes are alsofound to be strongly dressed by other electrons. The chargedensity of the dressed hole can be visualized in real space and isshown to deviate from the picture of noninteracting electrons.

The paper is organized as follows. The experimental andcomputational details are given in Sec. II and Sec. III,respectively. The comparison between experimental data andtheoretical results is presented in Sec. IV, where the physicalquantities related to the single-particle excitation can also befound. In Sec. V more discussions are given for addressing

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0

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experiment

planar-like

planar-like

2p1/2

2p3/2

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backgroundshake up

totalraw data

FIG. 1. (a) Structures of buckled-like and planar-like silicene, where the t-Si (red), b-Si (green), and h-Si (blue) are indicated. (b) MeasuredSi 2p XPS spectrum (filled dots) and fitting results by symmetric Voigt functions. The fitted α (blue), β (green), and γ (red) peaks togetherwith the background (orange) and shake-up (brown) contributions are presented. DFT-GGA binding energies are plotted by the same Voigtbroadening using the energies listed in Table I, and the area ratio of h-Si, b-Si, and t-Si is considered as 2:3:1 for both the (c) buckled-like and(d) planar-like silicene. Density of states of buckled-like and planar-like silicene with Gaussian broadening of 0.15 eV is shown in (e) and (f),respectively.

several DFT-related issues. In Sec. VI a summary is given,which concludes the paper.

II. EXPERIMENTAL

The XPS measurements were performed using synchrotronradiation source at Photon Factory BL-13B. The spectrawere recorded by a hemispherical electron energy analyzer(Scienta SES200). All the measurements were carried out at300 K in ultrahigh vacuum (UHV). The zero binding energywas taken at the Fermi edge of a tantalum foil attached tothe sample holder. Normal emission spectra were collected.The incident photon energy was 260 eV for Si 2p. TheZrB2 film was epitaxially grown on the Si(111) substrate bychemical vapor deposition in UHV at JAIST. An oxide- andcontamination-free epitaxial silicene monolayer was preparedon the ZrB2/Si(111) substrate by heating the sample at 1053 Kfor about 30 minutes in UHV.

To analyze the contribution of each Si atom from themeasured Si 2p spectrum (raw data), the choice of fittingfunctions becomes essential. In previous studies, the raw datawere fitted using asymmetric pseudo-Voigt functions for threeSi atoms and found to be consistent with the DOS of the

buckled-like silicene [9,22]. Regarding that the Si 2p corelevels are localized in energy away from the other states andthe major energy splittings are the gaps between 2p1/2 and2p3/2 orbitals, another good choice is to use the standardsymmetric Voigt functions that should be able to uncover therelevant excitation sources in Si surfaces [19–21]. However,the fitted peaks using symmetric Voigt functions resemble theDOS of neither the buckled-like nor the planar-like silicene.Having the puzzling discrepancy between experiment andtheory mentioned in Sec. I, it is then interesting to seewhether the fitted peaks using symmetric Voigt functions fordifferent photon energies could give consistent results withthe calculated absolute binding energies of the ground-stateplanar-like silicene.

The fitting results using symmetric Voigt functions revealthree sets of peaks labeled as α, β, and γ contributed fromthree different Si atoms. The results of the present studyare shown in Fig. 1(b) where each set contains two peakscorresponding to the 2p1/2 and 2p3/2 contributions. It can beobserved that the α and γ peaks have the smallest and largestbinding energies, respectively, together with the in-between β

peak in each angular momentum j contribution. In addition tothe symmetric Si 2p peaks, shake-up components [22] together

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SINGLE-PARTICLE EXCITATION OF CORE STATES IN . . . PHYSICAL REVIEW B 95, 115437 (2017)

with a Shirley-type background have also been considered. Thefitting results of α, β, and γ peaks of previously reported rawdata [22] using symmetric Voigt functions for three differentphoton energies are found to exhibit the same feature. For thesake of conciseness, the corresponding α, β, and γ peaks areshown in the Appendix, where the detailed fitting parameterscan also be found.

III. COMPUTATIONAL DETAILS

The first-principles calculations were performed using theOpenMX code [38], where the addition of a penalty functionalfor simulating creation of an atomic core hole and theexact Coulomb-cutoff technique for avoiding the undesiredinteraction between periodic holes were implemented [36].Although the developments allow us to access the energy ofsingle-particle excitation that takes into account the effectsof exchange and correlation triggered by the removal ofone electron, the approximation to the exchange-correlationfunctional still plays a role that could alter the results. In thisstudy, the generalized gradient approximation (GGA) [39] wasadopted. The norm-conserving relativistic pseudopotentialsand optimized pseudoatomic basis functions were used asadditional approximations to the all-electron problem [40–42].In the calculations with the presence of core holes, Si 2p corestates were relaxed during the SCF iterations. The spin-orbitcoupling was taken into account and responsible for the energysplitting between j = 1/2 and j = 3/2 angular momenta.Three, two, and two optimized radial functions were allocatedfor the s, p, and d orbitals for each Zr atom with a cutoffradius of 7 bohrs, respectively, denoted as Zr7.0-s3p2d2.For Si and B atoms, Si7.0-s2p2d1 and B7.0-s2p2d1 werechosen. A cutoff energy of 220 Ry was used for numericalintegrations and for the solution of the Poisson equation.The 2 × 2 k-point sampling was adopted for the (4 × 4)ZrB2(0001) unit cell whose in-plane lattice constant was set to4 × 3.174 A [13]. The slab with five Zr layers and four B layerswas studied and terminated by either the Zr layer or silicene.The vacuum thickness separating the slabs was set to 20 A.The core-level binding energies of the (4 × 4) ZrB2(0001)were found to converge with the supercell size in the treatmentfor metals, where the binding energies were calculated solelyin the N -electron system and would be consistent with thosecalculated involving the N and N − 1 electrons after reachinggood convergence against the supercell size [36]. The atomicpositions were relaxed without spin-orbit coupling until theforces were less than 2 × 10−4 hartrees/bohr. The optimizedgeometric structures were frozen for the calculations with thepresence of core holes.

IV. RESULTS

The structures of planar-like and buckled-like phases,obtained by the DFT calculations, are presented in Fig. 1(a).The total energy of the planar-like phase is lower than thatof the buckled-like phase by 272 meV per Si atom. Thebuckled-like silicene resembles the freestanding silicene [43]but the lower Si atoms are pushed up while locating on topof Zr atoms, denoted as t-Si, in comparison with the otherlower Si atoms locating above the centers of Zr triangles,

denoted as hollow-Si (h-Si). The higher Si atoms are immuneto further buckling and locate above the Zr-Zr bonds asbridging Zr atoms, denoted as b-Si. On the other hand, theplanar-like silicene possesses a different structure, where onlythe t-Si is protruding out leaving the others at similar heights,close to a planar structure. It can be expected that thesedifferent structures should give distinguishable single-particleexcitation energies of core states.

A. Single-particle excitation energy

The physical picture of single-particle excitation can beunderstood by studying the difference of physical quantitiesbetween N and N − 1 (or N + 1) particles in the many-electron system. Once a Si 2p electron is removed fromsilicene as a bare hole, the surrounding electrons that werecorrelated with the removed electron would act on, forexample, screening the positive charge of the hole in reducingthe electrostatic energy and bring the system to a new state. Thenew state should be described by the many-body eigenstatesof N − 1 electrons. To have long lifetime for the renormalizedhole, the best scenario is that the new final state belongsto a single eigenstate |m〉. The energy of the dressed hole(DH) can be considered as EDH = EN−1

m − EN0 , where E0

denotes the ground state. Obviously, once the dressed hole iscreated, the system immediately falls into the eigenstate |m〉with the total energy equal to EN

0 + EDH . After minimizingthe total energy of the system with the presence of the barehole introduced by the penalty functional, the DFT-proposedstate is then considered as the excited state |m〉. The obtainedtotal energy can be substituted for EN−1

m .In XPS experiments, the value of the binding energy

EB = μN + EDH is obtained, where μ denotes the chemicalpotential. For reaching good convergence of EB against thesupercell size in metallic systems, the binding energy canbe alternatively determined by Emetal

B = ENm − EN

0 [36]. TheEmetal

B ’s of Si 2p orbitals calculated on the (4 × 4) ZrB2(0001)substrate and the convergence test of h-Si of the planar-likephase in collinear calculations as well as the observed XPSpeaks are listed in Table I. Note that we directly investigatethe total energy difference via two SCF calculations (�SCF)for each binding energy, where no dynamical effects, likethose described by the diagrammatic processes within the GW

approximation, are explicitly calculated for the screening.In Figs. 1(c) and 1(d), the binding energies Emetal

B listedin Table I are plotted using the same Voigt broadening, andthe area ratio of h-Si, b-Si, and t-Si is considered as 2:3:1.Interestingly, the DFT-GGA-revealed peaks for the 2p1/2 and2p3/2 holes created in h-Si, b-Si, and t-Si of the planar-likephase shown in Fig. 1(d) agree quite well with the α, β, andγ peaks, respectively, in the absolute scale. In contrast, thet-Si Emetal

B of the buckled-like phase possesses the smallestvalue as presented in Fig. 1(c), which is inconsistent with theXPS measurements described in Sec. II and also in Fig. 1(b).This finding resolves the puzzling discrepancy in analyzingthe core-level binding energies between the experimental dataand those obtained from the ground-state planar-like phase.

Note that the previously reported XPS study compared thedata to the relative eigenvalues of Kohn-Sham orbitals of thebuckled-like phase, which is the information presented by

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TABLE I. Binding energies (EmetalB ) of Si 2p1/2 and 2p3/2 orbitals

of silicene on (4 × 4) ZrB2(0001) in the buckled-like (B-like) andplanar-like (P-like) structures as well as the fitting values of XPSpeaks in eV. The fitting values for different photon energies (PE) aregiven, respectively. The raw data for the PE at 130 eV, 340 eV, and700 eV are obtained from Ref. [22]. Emetal

B ’s of P-like h-Si 2pz orbitalsagainst supercell sizes from collinear calculations are also listed forshowing the convergence.

2p1/2 2p3/2

(4 × 4) h-Si b-Si t-Si h-Si b-Si t-Si

B-like EmetalB 99.33 99.39 99.14 98.61 98.70 98.45

P-like EmetalB 99.15 99.50 99.63 98.45 98.80 98.91

experiment α β γ α β γ

PE = 130 eV 99.30 99.55 99.67 98.69 98.94 99.06PE = 260 eV 99.26 99.50 99.66 98.64 98.88 99.05PE = 340 eV 99.34 99.59 99.77 98.72 98.97 99.15PE = 700 eV 99.31 99.56 99.71 98.69 98.95 99.09

P-like (2 × 2) (4 × 4) (6 × 6)h-Si 98.43 98.35 98.37

the DOS. The DOS of both phases is shown in Figs. 1(e)and 1(f), respectively. The energy sequence of Kohn-Shameigenvalues in the buckled-like phase is b-Si, t-Si, and h-Si,where the b-Si eigenvalue has the lowest value, while thesequence is t-Si, b-Si, and h-Si in the planar-like phase.These relative eigenvalues can be understood in terms ofthe Coulomb repulsion between orbitals. Assuming that theorbitals distribute their charge density from each atomic centerto its near neighbors, having more near neighbors would givestronger Coulomb repulsion and increase the energy. EachSi atom has three nearest neighbor Si atoms together withthe nearest neighbor Zr atoms. Guided by the structures inFig. 1(a), the coordination numbers of t-Si, b-Si, and h-Si canbe considered as four, three, and six in the buckled-like phaseand three, five, and six in the planar-like phase, respectively,which exactly map the energy sequences in the DOS. However,these energy sequences differ from the calculated absolutebinding energies. The Kohn-Sham eigenvalues also deviatefrom both the measured and calculated binding energiesby ∼9 eV in the absolute scale. The core-hole screeningfrom other electrons is responsible for giving rise to boththe observed XPS spectrum and calculated binding energies,which will be discussed in Sec. IV B and Sec. V.

B. Charge density of the dressed hole

We now consider the modification of charge densitydistribution via the creation of the core hole. The modificationinvolved in the single-particle excitation can be defined asnDH = nN−1

m − nN0 for representing the charge density of the

dressed core hole. Unlike the case of noninteracting electrons,the nDH is not purely negative in real space so that both holesand electrons can be created. The created electrons play anessential role in screening the holes whose major constituentis from the introduced penalty functional. For metallic systems,nDH can be defined as nN

m − nN0 + δn, where δn is regarded as

FIG. 2. Charge density modification, defined as nNm − nN

0 , ofplanar-like silicene (yellow). The positive (red) and negative (blue)contributions indicate the amounts of charge density that need to beadded and removed from nN

0 , respectively. The charge-density surfaceis plotted at 0.001 e/bohr3. The cases with core holes created in(a) h-Si 2p1/2, (b) b-Si 2p1/2, and (c) t-Si 2p1/2 are presented. The2p3/2 results are similar to the 2p1/2 ones (not shown).

dilute electron gas. The integration of δn over the whole systemshould be exactly −1. The major response of charge densityaround the bare hole can then be focused on nN

m − nN0 , where

the positive and negative values reflect the needed electronsand holes to be created in the ground state, respectively.

The charge density of the dressed hole can be visualizedin real space. The nDH of the planar-like phase withoutpresenting δn is plotted in Fig. 2. The positive and negativecontributions corresponding to the addition and removal ofelectrons from the ground state, respectively, can be identified.The spherical shape of positive contribution surrounding theSi atom with a core hole can be seen in Fig. 2, which screensthe positive charge of the core hole. The deviation of eachdressed hole from the atomic eigenstate can also be recognizedfrom the charge density distribution that shows large positiveand negative modifications around the neighboring atoms,including the top-layer Zr ones. This clearly supports that thebare holes are strongly dressed in consistency with the claimedessential role of the final-state effects in the XPS spectra [25].The difference of nDH between 2p1/2 and 2p3/2 states canreflect the effect of core-level spin-orbit coupling. At longdistance from the core, there is no significant difference asshown by the 0.001 e/bohr3 charge density surface in Fig. 2,reflecting the electrostatic screening of a positive point charge.

In DFT the total energy is uniquely determined by thecharge density; the effect of taking into account the chargedensity of fully dressed holes enhances the h-Si Emetal

B inthe buckled-like phase and suppresses the t-Si Emetal

B in theplanar-like phase in comparison with the respective DOS. Asa result, the energy sequences of the peaks in both phases arechanged, especially in the buckled-like phase. Although therelative values of the planar-like phase in the DOS are similarto those in Emetal

B ’s and can be understood therein, having theaccurate modification of the charge density distribution givesthe well separated 2p1/2 and 2p3/2 peaks in the absolute values

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of binding energies that reach good agreement with the XPSspectrum.

V. DISCUSSION

The calculated absolute binding energies of the planar-likephase are shown in good agreement with the XPS experiments.This implies that the total energy differences obtained inthe DFT-GGA calculations are able to describe the poles ofone-particle Green’s function of epitaxial materials. Recallthat the ground-state total energy and charge density of amany-electron system are proven to be describable via a set ofnoninteracting Kohn-Sham orbitals in the framework of DFT[11,12]. The achievement has led to successful predictionsof the ground-state properties, and DFT continues as oneof the state-of-the-art methods in studying condensed matter[44]. Our study of epitaxial silicene gives an example ofsuccessful applications of DFT in studying excited statesof many-electron systems within the ground-state-type SCFcalculations.

The issue concerning the physical meaning of Kohn-Sham orbitals has been frequently discussed [24,45–47]. Itis known that Kohn-Sham eigenvalues cannot be directlyused to compare with the quasiparticle energies [15,35,47]that are measured in the photoelectron spectra [16–21]. Thismakes sense since creation or annihilation of a single-particleeigenstate in an interacting many-body system must causestrong or weak but nonzero correlation, and the involveddegrees of freedom in the many-body multiplets must bemuch larger than the number of single-particle eigenstatesin general. Nevertheless, the highest occupied orbital of asystem has been proven to deliver the ionization energy[48,49]. Each eigenvalue of the Kohn-Sham orbital is alsomathematically proven to connect to the derivative of thetotal energy with respect to its occupation [50]. Our studyadvocates that the single-particle Kohn-Sham orbitals notonly construct the ground-state charge density but are eligiblefor representing the bare hole in describing the core-levelsingle-particle excitation. By adding a penalty functional tothe designated Kohn-Sham orbital through a projector, the newset of Kohn-Sham orbitals is able to screen the bare hole andallows accessing the excitation energy of the many-electronsystem in the absolute scale even though the eigenvaluesthemselves could be different from the total energy differences.

We have defined the charge density of the dressed corehole nDH in studying the charge density modification causedby the creation of the core hole. For the metallic systems,the integration of nN

m − nN0 over the whole system is zero

with equal amounts of positive and negative values. Themodification in charge density can then be reflected by nN

m,0 ≡∫ |nNm(�r) − nN

0 (�r)|d�r integrating over the studied supercell.As listed in Table II, nN

m,0 is on the order of 3 electrons,which means that ∼1.5 holes containing the created one and∼1.5 electrons are introduced in the ground state. The ∼1.5electrons are responsible for screening the created hole. In theactual situation of the metallic system of N − 1 electrons, theelectrons that screen the holes are mainly contributed fromthe electrons over the whole system; this is the dilute δn wehave illustrated before. For comparison, the ntotal

DH defined as∫ |nN−1m (�r) − nN

0 (�r)|d�r is also listed in Table II. Although

TABLE II. The nNm,0, defined as

∫ |nNm (�r) − nN

0 (�r)|d�r , and ntotalDH ,

defined as∫ |nN−1

m (�r) − nN0 (�r)|d�r , of buckled-like (B-like) and

planar-like (P-like) silicene on (4 × 4) ZrB2(0001) in units of thenumber of electrons.

2p1/2 2p3/2

h-Si b-Si t-Si h-Si b-Si t-Si

B-like silicene (nNm,0) 3.15 3.09 3.03 3.18 3.12 3.08

B-like silicene (ntotalDH ) 3.60 3.61 3.57 3.63 3.64 3.62

P-like silicene (nNm,0) 3.07 3.03 3.13 3.12 3.07 3.16

P-like silicene (ntotalDH ) 3.57 3.57 3.64 3.61 3.61 3.67

we need a larger supercell to reach better convergence inthis treatment, the 0.001 e/bohr3 charge density surfaces aresimilar to those shown in Fig. 2 and the ntotal

DH ’s are also on theorder of 3 electrons. An estimation of leading magnitude inntotal

DH can be concluded as follows: 1 hole is from the introducedcore hole, 1 electron is in response to screening the hole,and the source of that electron is from the dilute electrongas distributing over the whole system, which correspondsto 1 hole that needs to be created in the ground state. Ourstudy shows the importance of existence of both signs in nDH

for delivering the accurate values of binding energies in theinteracting many-electron systems.

VI. SUMMARY

Studies of creation of core holes and the induced cor-relations in solids are important for understanding theirconstituent atoms, chemical environment, electronic states,and various physical properties. By introducing the additionof a penalty functional to simulate a core hole and the exactCoulomb-cutoff technique to avoid the undesired interactionsbetween periodic images of the created core hole, we proposean approach to study the single-particle excitation basedon the �SCF methods. The core-level states in silicene onZrB2(0001) have been studied by calculating the many-bodytotal energies and charge density directly within the frameworkof DFT. From that, the addition and removal attributes ofcharge density of the dressed core hole that cannot be revealedby a single-particle eigenstate alone are demonstrated. Thepuzzling discrepancy between the XPS spectrum and theDOS revealed by Kohn-Sham orbitals of the ground-stateplanar-like phase has been resolved by directly comparing theabsolute binding energies that are obtained from total energydifferences, not the single-particle eigenvalues. The core holesare found to be strongly dressed by other electrons evidentfrom the large modifications in the charge density involvingsurrounding atoms, and the energy sequence is also changedin comparison with DOS. The good agreement between theoryand experiment not only resolves the puzzling discrepancy butalso highlights the success of DFT in fingerprinting the bindingenergies of surface atoms including spin-orbit coupling. Thiswork paves a way for future exploration of single-particleexcitation of interacting electrons in various materials distinctfrom the methods based on the diagrammatic perturbationtheories.

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TABLE III. Fitting parameters using symmetric Voigt functionsfor different photon energies (PE). The experimental raw data at260 eV are obtained from the present study while the raw data at130 eV, 340 eV, and 700 eV are from Ref. [22]. The binding energies(EB ), the full width at half maximum of Lorentzian (WL), and the fullwidth at half maximum of Gaussian (WG) for each α, β, or γ curveare given in units of eV. The (area) intensity ratio (R) is also listed.

PE = 130 eV EB (2p1/2) EB (2p3/2) WL WG R

α 99.302 98.688 0.056 0.135 3.69

β 99.551 98.937 0.056 0.159 5.58

γ 99.670 99.056 0.056 0.202 1.00

PE = 260 eV EB (2p1/2) EB (2p3/2) WL WG R

α 99.257 98.639 0.062 0.174 2.47

β 99.501 98.883 0.062 0.192 3.65

γ 99.665 99.047 0.062 0.267 1.00

PE = 340 eV EB (2p1/2) EB (2p3/2) WL WG R

α 99.338 98.718 0.056 0.145 3.34

β 99.590 98.970 0.056 0.187 6.76

γ 99.766 99.146 0.056 0.245 1.00

PE = 700 eV EB (2p1/2) EB (2p3/2) WL WG R

α 99.312 98.693 0.067 0.204 1.78

β 99.565 98.946 0.067 0.191 2.62

γ 99.710 99.091 0.067 0.382 1.00

ACKNOWLEDGMENTS

We are grateful for the use of supercomputers at JAIST.This work was supported by Japan Society for the Promotionof Science Grant-in-Aid for Scientific Research on InnovativeArea “3D Active-Site Science” and Priority Issue (Creationof new functional devices and high-performance materials tosupport next-generation industries) to be tackled by usingPost K Computer, Ministry of Education, Culture, Sports,Science and Technology, Japan. This work has been performedunder the approval of the Photon Factory Advisory Committee(Proposals No. 2009S2-007, No. 2012G-610 and No. 2015S2-008).

APPENDIX: FITTING PARAMETERS

The fitting parameters for different photon energies aregiven in Table III. The measured Si 2p spectra with the photonenergies at 130 eV, 340 eV, and 700 eV are obtained fromRef. [22] while the spectrum at 260 eV is from the presentstudy. The fitted α, β, γ , background, and shake-up peakstogether with the measured raw data are presented in Fig. 3.

0

5

10

15

20

25

Inte

nsit

y (a

rbit

rary

uni

t)

0

5

10

15

20

25

Inte

nsit

y (a

rbit

rary

uni

t)

100 99.5 99 98.5 98Binding Energy (eV)

100 99.5 99 98.5 98Binding Energy (eV)

100 99.5 99 98.5 98Binding Energy (eV)

0

5

10

15

20

25

Inte

nsit

y (a

rbit

rary

uni

t)

αγ

β

(b)

(a)

(c)

Photon energy = 130 eV

2p1/2

2p3/2

Photon energy = 340 eV

Photon energy = 700 eV

backgroundshake up

totalraw data

FIG. 3. Measured Si 2p XPS spectra (filled dots) obtained fromRef. [22] and fitting results by symmetric Voigt functions for photonenergies at (a) 130 eV, (b) 340 eV, and (c) 700 eV. The fitted α (blue),β (green), and γ (red) peaks together with the background (orange)and shake-up (brown) contributions are presented.

The larger Gaussian widths of the γ curves could be thesignature of the peculiar position of the pushed-up t-Si atomin the planar-like structure. Although the electron interferencegives different patterns at different wavelengths, the intensityratios collected from the normal emission do not deviate fromthe atomic ratio 2:3:1 at different photon energies significantly.

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